Fuzzy control of continuous-time recurrent fuzzy systems

This article presents a synthesis method for stabilization of equilibria in continuous-time recurrent fuzzy system. It is first shown how to obtain a hybrid system representation from the given linguistic differential equations defining the recurrent fuzzy system. Based on this, the controller synthesis algorithm presented is then a two step procedure. By means of the synthesis step, a fuzzy controller is obtained by solving a single optimization problem, which guarantees that no chattering effects will occur in the controlled recurrent fuzzy system. Stability of the equilibrium is then proven by a verification procedure utilizing sum of squares methods. A performance optimization by means of additional polynomial controllers is discussed. The main advantage of our method relies in the computational efficiency of the synthesis problem as well as in the linguistic interpretability of the resulting controller. In addition, chattering effects are proven not to occur.